In one universe, this blog is about quantum mechanics. In another universe, it is not.

One of the dreams regularly involved a tennis tournament played on a mountaintop in Peru. Another had an origami master who was the operator of an armored personnel carrier. Yet another consisted of an Australian women’s rugby coach who moved to Serbia, opened a brewery, and wrote a novel based on the life of Python of Byzantium (Πύθων ὁ Βυζάντιος).

The worst of these dreams, however, was a nightmare which tormented the man periodically. In this nightmare, there was a xylophone made from human bones: finger bones for the high notes on the right, down to an enormous femur for the lowest note on the left. In this nightmare, the man was invariably tied to the xylophone with shigawire, while a demonic musician played something execrable (such as Vivaldi’s Four Seasons). At the climax of the music, just when the man was on the point of being driven entirely insane, the ghost of Warren G. Harding poured grape juice onto the xylophone from an amphora made of jade.

At this point the man always awoke with a start, in a cold sweat, sometimes screaming, sometimes crying.

It goes without saying that the man developed a lifetime phobia of grape juice being poured onto xylophones. And worse: he developed a fear of almost any juice product being dumped onto any percussive mallet-based instrument.

He avoided Kindergarten classrooms, for who could say that little Timmy might not pour his juicebox onto that glockenspiel? He avoided performances of Danse Macabre by Saint-Saëns, for might not the percussionist have a flask of wine which could spill forth? And forget ever going to see the Rolling Stones in concert: might not a band member spill a screwdriver onto the marimbas during “Under My Thumb”? All told, the man’s phobia represented a very minor, but non-zero, inconvenience.

Our story would be of little interest were it not for the fact that the man became Emperor of the World. How this was achieved is of no consequence to this parable; suffice to say that the man lied, preened, stole, and schmoozed his way to the top. But once he was in power, the now-Emperor decided that he could now rid himself of fear, by passing a law. The law was presented thus:

As Emperor of the World I hereby ban the pouring of grape juice onto xylophones. Anyone caught committing such a traitorous, cowardly act, will face the full wrath of our justice system, and be imprisoned for not more than 33 years.

The Emperor released this edict and went to bed content, confident that his nightmares were over.

But there were unintended consequences.

Most people had never, in their wildest fantasies, entertained the notion of pouring grape juice onto xylophones. The whole concept never crossed their minds. But now, with the Emperor explicitly banning the practice, the pouring of grape juice onto xylophones (PGJOX) became A THING. Suppose you wanted to irk the Emperor, get under his skin, be a gadfly, protest his policies. What better way, than PGJOX? Whereas before the Emperor clawed his way to power, there was not a single case of PGJOX, after the edict there were thousands of such cases.

The Emperor was too dense to realize that his law had caused all that grape juice to be poured. Indeed, the ballooning of PGJOX cases reaffirmed his pre-conceived notion that PGJOX was A THING, and had always been A THING, and so his law was justified. There was a vicious cycle: the more he railed against PGJOX, the more people performed the act he hated; this in turn caused him to rail against PGJOX all the more.

What became of the Emperor? And what became of the law? And what became of pouring grape juice on xylophones? In the first case, his nightmares returned, his dreams became indistinguishable from reality, and we are still to this day (centuries later) recovering from the 30-year rule of the Mad Emperor. Of course, the law banning PGJOX was repealed eventually, but (interestingly) pear juice is still poured onto vibraphones every Nov. 30 in parts of Alberta and Saskatchewan (on Banff Day).

Moral: if you’re a lawmaker, and there’s some strange act that makes you uncomfortable, then shhhhhhh…don’t do anything. Don’t bring attention to it. Passing a law against your pet peeve is just lighting a match and handing it to your opponents.

There’s a lot of talk these last few days of how horrible it would be if, for example, Penn State wins the Big Ten championship but doesn’t make the college football Final Four playoff. This would happen if, say, Washington (the current #4) loses to Colorado in the Pac-12 championship. Presumably, then, Michigan (now currently #5) would move up into the #4 slot, leaving the Nittany Lions crying into their Wheaties.

Why would this (ostensibly) be horrible? Well (the argument goes) you’d then have two Big Ten teams (Ohio State and Michigan) in the playoffs who didn’t even win their conference. Some people think this would be a travesty.

I disagree. Winning (or not winning) a conference is essentially meaningless. That’s because it’s entirely possible to win the conference with a shitty record.

First, we have to discuss how the Big Ten champ is chosen. There are 14 teams in the Big Ten, not 10. (We’re already in Twilight Zone territory here). 7 of the teams are in the West division, and 7 are in the East. Each year, each team plays 4 non-conference games, and 8 conference games; of those 8, 6 are in the same division, and 2 in the other division. The winner of the West will play the winner of the East to determine the Big Ten conference champ.

Suppose, in the East, Michigan, Ohio State, and Maryland all post 11-1 records; each losing only one division game to one of the other two. Based on arcane tie-breaks, one of these (presumably) good teams will be invited to the Big Ten championship. Let’s say it’s Maryland.

In the West, however, imagine that all 7 teams have identical 3-9 records. They achieve this by losing all non-divisional games, and splitting their West division games 3-3. One of these (crappy) teams will go to the Big Ten championship game by tie-break. Let’s say it’s Iowa.

So it’s Maryland (11-1) vs. Iowa (3-9). Maybe Iowa wins on a fluke (Maryland’s QB gets the flu, or a ref gives the game to Iowa by awarding a 5th down…these things happen). Despite this head-to-head result, is anyone really going to rank the now 4-9 Iowa Hawkeyes over the 11-2 Maryland Terrapins? Of course not.

Here’s the mathematical reason that conference championships are meaningless: all they tell you is that you’re the best team out of a subset of teams. And that doesn’t really tell you much at all.

Suppose we had a tournament for BIG COUNTRIES. Who would you rank among the top BIG COUNTRIES? My top four would be Russia, Canada, USA, and China. “But wait!” says Algeria. “I won the Africa division! And the USA is smaller than Canada and so didn’t even win its division!”

If we want to pick the BIG COUNTRIES, then being the biggest country in your continent is meaningless. Similarly, if we want to find the best teams, finding the best teams in conference divisions is meaningless.

One way to mitigate this problem is to eliminate conference divisions entirely. In the hypothetical scenario mentioned above, if the Big Ten just had one 14-team division, then Iowa would stay home and Maryland would play Michigan (say) for the conference title. Still not perfect, but we’d definitely know then that a good team had won the conference.

I’m not lobbying for any sort of change in the NCAA playoff selection rules. I have every expectation that the committee will do the right thing, regardless of whether Washington wins or not. Their ranking Ohio State #2 despite not even going to the Big Ten title game is indicative of that. What I am advocating for is for people to shut up about conference champions.

Hey, Algeria: just because you’re the biggest country in Africa doesn’t make you a top-4 country.

When I need comfort, this is the best piece of music I can imagine. It’s one long movement. It’s one continuous narrative. There is no suspension of disbelief required, by which I mean you don’t really hear individual instruments as instruments, or hear the whole orchestra and think “that’s an orchestra”. You forget you’re listening to a performance at all. You forget you’re listening to something man-made called “music”. It’s almost as if you’re listening to perfection, translated into the medium of music. The notes swell and ebb, and you wander through a beautiful yet haunting landscape. When every climax is reached, when every section finds its conclusion, the music evolves gradually, and a new summit is attempted, a new path is taken. But the previous sections don’t end; they become (in turn) the backgrounds for what lie before you. Listening to the 7th is like hiking a ridge line in the mountains, cresting apex after apex, but your previous climbs are always behind you, receding only gradually into the past. At many points in the journey, you think you’ve reached the top of the mountain, only to see the sun glint off a snowy peak in the distance, and realize you can yet climb higher. The ending is abrupt and resigned, like freezing to death on the mountaintop. If you cry, it’s just the cold wind in your eyes.

The NCAA should go to a Swiss-system for college football. And I don’t mean for the playoffs; I mean for the entire season.

First of all, here’s a brief primer on what the Swiss-system is. I don’t think I can explain it better than the hive mind on Wikipedia, so here’s a quote:

“A Swiss-system tournament is a non-eliminating tournament format which features a predetermined number of rounds of competition… In a Swiss tournament, each competitor (team or individual) does not play every other. Competitors meet one-to-one in each round and are paired using a predetermined set of rules designed to ensure that each competitor plays opponents with a similar running score, but not the same opponent more than once. The winner is the competitor with the highest aggregate points earned in all rounds.”

Such systems are very common in chess tournaments, and also used in backgammon, squash, and eight-ball tournaments. I’ve never heard of them being used in team sports, which is a pity.

If I were Emperor of the World, here’s how I would implement the Swiss-system for college football. At the beginning of the season, I’d rank the 128 FBS teams (teams that normally are bowl eligible) from #1 to #128. (Well, I probably wouldn’t rank the teams personally, but I’d have a computer and/or a committee rank the teams much as the BCS does now.) The great thing is that a ranking of #1 vs. a ranking of #5 (say) at the beginning of the season wouldn’t matter much at all.

The first week of the season, #1 would play #65, #2 would play #66, and so on. For illustrative purposes, if we based seeding on the current NCAA rankings (as of Nov. 7, 2016), we’d have Alabama (#1) playing Southern Mississippi (#65), Michigan (#2) vs. Texas Tech (#66), Clemson (#3) vs. Georgia (#67), Washington (#4) vs. NC State (#68), and so on, down to California (#64) vs. Florida Atlantic (#128). Every higher-ranked teamed would be favored of course, but you’re going to get plenty of upsets: every one of the matchups I just (arbitrarily) presented would be a decent game. Gone would be the days when an Alabama would play a non-FBS Western Carolina for their first game and win 49-0 to pad their resume.

Starting with week #2, things are already interesting. Every week after the first, each team plays another team with the exact same record (if possible). Continuing with my example, and assuming that all the higher ranked teams won in week 1, you’d already have on the table Alabama (#1) vs. Troy (#33), Michigan (#2) vs. Tulsa (#34), Clemson (#3) vs. Minnesota (#35), etc. None of these games are cake-walks by any means (for perspective, the current records of Alabama, Michigan, and Clemson are all 9-0, but the current records of Troy, Tulsa, and Minnesota are 7-1, 7-2, and 7-2, respectively.)

Here’s the thing: starting with week 2, every single game in college football is a competitive game. And starting around week 4, every single game is almost evenly-matched. We’ve eliminated the all-too-common problem with the current system: that the top teams really only play 2 or 3 meaningful games a year.

Suppose we were using the Swiss-system, and we were making the matchups for the coming week’s games (Nov. 12). What games would be on tap? Well, there are currently 5 undefeated teams, which in a Swiss-system would be very unlikely after 9 weeks. Just for fun let’s assume that it’s possible, but let’s ignore Western Michigan (no way they’d go 9-0 if they faced a few good teams). With Alabama, Michigan, Clemson, and Washington all 9-0, this week’s marquee matchups would be Alabama vs. Washington, and Michigan vs. Clemson. It’s likely that next week you’d have Alabama facing Michigan. This, in early November!

The good matchups continue all the way down the line. One-loss teams would all face each other, and you’d perhaps have games like Louisville vs. Ohio State. Even at the bottom of the barrel, with a Rice playing a Florida Atlantic, the games would be evenly-matched. This would be great for fans, because as it stands, when a Rice fan attends a game, they fully expect a loss; but with a Swiss-system, that same fan can be hopeful for at least a 50-50 shot at winning.

At the end of the season, an undefeated team would be almost impossible. It’s likely you’d have 3 or 4 teams that were 10-2, and they’d all have already played each other. That’s when a playoff would kick in.

For the playoff, we’d have the 4 (or better yet, 8) teams with the best records play each other in a standard elimination format. At this point, it wouldn’t matter if they’d already faced each other in the regular season; rematches at this point would be desirable. The great thing is that these teams would all be excellent teams. In a Swiss-system, if you go 10-2, facing tougher opponents every single week, no one can argue you aren’t one of the best teams in the country. Built into the Swiss-system is an important feature, which is that basically, every team at the end with a similar record faced a similar strength of schedule.

This is important, for in the current system, teams which are 12-0 can be left out of the playoff discussion if they’d didn’t play any good teams. That’s never struck me as particularly fair. If my team goes 12-0 and doesn’t get to the playoffs, then that means the team never even had a theoretical shot at making the playoffs to begin with. What’s the point, then? It’s a sordid fact that in the current system, there are only 30 or so teams that can ever even theoretically make it to the playoffs in a given year. I’m sorry, Florida Atlantic, but if you go 12-0 next year you ain’t playing in a major bowl game.

There are obviously a few objections one could raise to my brilliant scheme. Let’s address them.

What about logistics? How in the world could you have teams flying around the country, facing each other, planning trips on only a week’s notice? Well, as Emperor, it wouldn’t be my problem. But in any case, it’s the 21st century for Xenu’s sake, so I think with some 747’s and the internet, it could be done.

What about revenue? If Western Carolina doesn’t get to play and get crushed by Alabama, then Western Carolina loses out on some big time TV money! OK, sure, but the games will in general be much, much more competitive, and many more fans will go to see WCU home games since they finally have a chance to win. I really believe TV revenue would be up across the board. We could even implement a TV revenue-sharing scheme, but that’s a topic for another day.

What about rivalries? Well, what about them? The current system doesn’t give a fuck about them in any case. I can’t even keep track of who’s in what conference these days. (Syracuse is in the ACC? When did that happen? They’ll always be a Big East team to me.) With a Swiss-system, conferences become meaningless, and I say good riddance.

As for the handful of actual rivalries that still exist, and haven’t become jokes, such as Army vs. Navy (come to think of it, that has become a joke) or Alabama vs. Auburn, you could have the teams play an extra game in mid-December that doesn’t really count for anything. If you think it’s unfair that a team has to play an extra game compared to other teams, well then, why not have every team pick a greatest rival that they have toplay every year? Hell, these games might even be the first games of the year, a sort of pre-season-type game, and the results don’t affect the Swiss-system per se, but the results might inform the seedings. So Navy plays Army (a joke game, usually) but if Navy loses, we might initially rank them a little lower than otherwise.

Would any of this ever happen? Not one chance in a million. But it’s fun to speculate about. And mark my words, in the universe(s) where I actually do become Emperor, initiating an NCAA football Swiss-system is one of my first magnanimous acts.

Don’t get me wrong; the theorem is fairly useless. The proof itself is trivial. But the fact that I came up with the proof, in my head, makes me proud…mostly because I’m a physicist, not a mathematician.

Here is the theorem:

Square any odd integer greater than 1, and then subtract 1. The result is evenly divisible by 4.

I’ll leave the proof to you, for fun. Do it in your head!

This is what theoretical physicists daydream about on 7 hour car rides.

I spent a ridiculous amount of time writing my last blog post. I mean, it was almost 5000 words. Who writes 5000 words just for fun? But luckily, all that work will yield not just one, but two (or maybe even more) blog posts. Just as PhD’s mine their dissertations for journal articles, I will mine the last post for more nuggets of symphonic information. We will count down the 100 symphonies ever written. Most of the work has already been done: I’ve ranked every numbered symphony I could think of (spoiler alert: Sibelius has the top 2 spots!) but there are some symphonies I’ve left out. We need to add some works numbered 10 and beyond; and we need to add a few symphonies without numbers at all. Likewise, we need to get rid of some of the “throwaways”. Sorry, Haydn #9.

What, exactly, is a symphony? I consider it a large-scale work for orchestra, for which soloists don’t play a major part. That’s a pretty broad definition, but it excludes things like Bartók’s Concerto for Orchestra, Bach’s Brandenburg Concertos, and Beethoven overtures. There’s some subjectivity here: why exclude Lenore III when, in actuality, it’s longer than some Mozart symphonies? I don’t have a good answer except to say that Lenore III wasn’t meant to stand on its own…it was meant to be part of an opera. A symphony should be self-contained.

One further point. I’m not going to rehash all of the symphonies from the previous post. I am going to use the scores from that post, but in order to keep this post under 5000 words I’m going to limit myself to one sentence only for each symphony.

Here’s the countdown:

Bruckner Symphony #1

Not the strongest Bruckner symphony, but worth a listen for the promise it conveys.

Schumann Symphony #4

Schumann’s best symphony is well-constructed but kinda forgettable.

Beethoven Symphony #6, “Pastoral”

Most people like it, but it’s too cheery for me (in a “drunken centaur” kind of way).

Tchaikovsky Symphony #1, “Winter Dreams”

Not Tchaikovsky’s best, but sprightly and with a triumphant ending.

Shostakovich Symphony #15

A demented toy shop: just listen for the quotes from the William Tell Overture.

Gottfried Helnwein, Untitled

95. Borodin Symphony #2

Good and bad in equal measure, it depends upon your mood.

Beethoven Symphony #3, “Eroica”

The first memorable Beethoven symphony, but the funeral march is boring.

Tchaikovsky Symphony #2, “Little Russian”

More serious, slightly improved version of Tchaikovsky’s 1st.

Bax Symphony #7

Bax tries to emulate Holst’s The Planets, but only partly succeeds.

Piston Symphony #7

Almost like a movie soundtrack, with hints of Copeland.

Haydn Symphony #94, “Surprise”

Stereotypical late Haydn, which can be good or bad.

Mahler Symphony #3

A glorious, epic mess; the singing parts are just weird.

Schubert Symphony #6, “Little”

Even a weaker effort of Schubert is better than most people’s best.

Shostakovich Symphony #2, “October”

Experimental, random, chaotic, but ultimately triumphant.

Mahler Symphony #1

All-encompassing journey to a primordial alien world, marred by the presence of an insipid children’s song.

Glass Symphony #9

This is what happens when Glass tries to sound more like Sibelius or Bruckner.

Bax Symphony #6

This muscular symphony could be the soundtrack to Conan the Barbarian.

Brian Symphony #1, “Gothic”

Gargantuan, beautiful, and over-long.

Mahler Symphony #8

Mahler tries to make his own “Beethoven’s 9th” but dispenses with the foreplay.

Bruckner Symphony #3, “Wagner Symphony”

The first fully mature Bruckner symphony…serious and masculine.

Dvorak Symphony #8

Happy and mature…a hike for grown-ups.

Tchaikovsky Symphony #4

“A sleigh ride through Siberia”, and proof that Tchaikovsky just kept getting better.

Mozart Symphony #39

Underrated Mozart symphony that matches the heft and polish of the more famous last two (#40 and #41).

Prokofiev Symphony #7

Melancholy and percussive, and proof that Prokofiev wrote more than just the “Classical” symphony and Romeo and Juliet.

Shostakovich Symphony #12, “The Year 1917”

Some call it a film score looking for a movie, but it sounds good to me.

Sibelius Symphony #1

The first sign that Sibelius is The Chosen One.

Mendelssohn Symphony #4, “Italian”

It’s like crème brulee that’s been sitting out for an hour or so.

Glass Symphony #3

The best symphony by Philip Glass.

Haydn Symphony #88

This takes refinement to a whole new level.

Vaughn Williams Symphony #8

Great and otherworldly, but the ending has me thinking of all the Who’s singing down in Whoville.

Prokofiev Symphony #1, “Classical”

Hey, look Ma, I can write a classical Haydnesque symphony in the 20th century!

Vaughn Williams Symphony #5

Pastoral and Faux-Sibelius, with Hobbits.

Vaughn Williams Symphony #6

Hey, I know, let’s just depress everyone with this “nuclear wasteland” ending.

Mahler Symphony #6, “Tragic”

It’s got some hammer blows in there somewhere?

Mahler Symphony #5

A sublime Adagietto padded by an hour of epic Mahlerian mush.

Sibelius Symphony #3

Leaner and more focused, this is a new direction for Sibelius.

Shostakovich Symphony #10

Tense and colorful and oppressive, like a Soviet propaganda poster brought to life.

Mahler Symphony #7

Strange, bleak, demonic, and then…triumphant?

Mozart Symphony #35, “Haffner”

Mozart tries something a little…bigger.

Hovhaness Symphony #63, “Loon Lake”

I have no idea where Loon Lake is, but I want to go there now.

Haydn Symphony #82, “The Bear”

My favorite lesser-known Haydn symphony.

Bruckner Symphony #6

Like Bruckner’s 5th on Xanax.

Bruckner Symphony #4, “Romantic”

The age of chivalry made into music.

Shostakovich Symphony #9

Goofy, sinister, vigorous, and off-putting.

Tchaikovsky Symphony #5

Despair gives way to triumph.

Gottfried Helnwein, Midnight MIckey

Schubert Symphony #5

You could call this “Mozart’s 42nd”.

Schubert Symphony #8, “Unfinished”

Pristine, flawless, menacing…then peaceful.

Shostakovich Symphony #1

A stroll through a museum of artworks by mental patients.

Haydn Symphony #26, “Lamentatione”

Why didn’t Haydn write more symphonies in a minor key?

Hovhaness Symphony #22, “City of Light”

Harmonious and magisterial.

Mozart Symphony #38, “Prague”

The first Mozart symphony with real gravitas.

Bruckner Symphony #7

Great Adagio, even if Hitler liked it, too.

Gottfried Helnwein, Epiphany I

Sibelius Symphony #6

It’s like waking up to a foggy dawn in the Smokies, to discover autumn’s first frost.

Beethoven Symphony #4

The most underrated Beethoven symphony.

Tchaikovsky, Manfred Symphony

This is so good, how come no one has ever heard of it?

Nielsen Symphony #4, “The Inextinguishable”

Eclectic, disturbing, psychological, with a timpani battle!

Khachaturian Symphony #3

“Raw and strident” …it’s a single movement, dominated by an organ and 15 (!) trumpets.

Shostakovich Symphony #8

Like a vacation in East Germany.

Schubert Symphony #3

I challenge you not to like this.

Mahler Symphony #10

Ah, what might have been…

Bizet, Symphony in C

Here’s a teenager putting the rest of us oldsters to shame.

Nielsen Symphony #5

Nielsen tops his 4th with an even more war-like symphony.

Rachmaninoff Symphony #2

A harmonic mosaic that somehow conveys poignancy, joy, and sadness at the same time.

Dvorak Symphony #7

My favorite Dvorak symphony other than the 9th…I wish I knew why.

Ives Symphony #4

It’s like a church service with goblins besieging the place.

Haydn Symphony #49, “La Passione”

Haydn + minor key = good.

Mozart Symphony #40

Mozart + minor key = good.

Górecki Symphony #3, “Symphony of Sorrowful Songs”

Threadbare songs of infinite sadness.

Tchaikovsky Symphony #6, “Pathetique”

Tchaikovsky’s best; there’s just so much going on here.

Haydn Symphony #39

Strum und Drang…must I say this was in a minor key?

Strauss, Also Sprach Zarathustra

OK, maybe this isn’t a symphony, but holy shit….please, please, listen to more than just the cliched opening two minutes!

Mahler Symphony #9

Funny, how much of the best Mahler is the Mahler that sounds most like Bruckner.

Franck, Symphony in D minor

A French organist tries his hand at symphonic writing, and scores a home run.

Mozart Symphony #29

Maybe the best opening movement of any Classical symphony.

Mahler Symphony #2, “Resurrection”

Mahler’s best.

Beethoven Symphony #5

Skip the first movement if you want to hear this with fresh ears.

Mozart Symphony #25

Agitated, syncopated, minor key…are we sure this was written in 1773?

Shostakovich Symphony #7, “Leningrad”

Trump’s ascent made into music: the banality of evil.

Shostakovich Symphony #11, “The Year 1905”

Highly visual and emotional tour-de-force.

Dvorak Symphony #9, “From the New World”

Maybe the catchiest symphony of all time.

D’Indy, Symphony on a French Mountain Air

Like a picnic in the Alps, in springtime.

Brahms Symphony #1

Some call it “Beethoven’s 10th” and that’s not far off the mark.

Brahms Symphony #4

Better than the 1st, by a hair…Brahms proves here that rigid structure and control can still yield immense beauty.

Saint-Saëns Symphony #3, “Organ Symphony”

The organ’s entry in the finale is spectacular…and is that a fugue?

Bruckner Symphony #8

Apocalyptic in every sense of the word.

Berlioz, Symphonie Fantastique

A fever dream: Downton Abbey on ecstasy, with some Satanism thrown in for good measure.

Beethoven Symphony #7

Sublime.

Mozart Symphony #41, “Jupiter”

Sounds simple, but if you look at the 4th movement along with the score, your mind will be blown by how complicated the fugue is!

Even though it predates World War II, this is an invasion by Nazis, turned into music.

Bruckner Symphony #9

Unrequited longing…unresolved harmonies…and then it—

Sibelius Symphony #2

Has the greatest musical orgasm ever written.

Beethoven Symphony #9

Encompasses all of human experience.

Sibelius Symphony #5

The best symphony ever written.

Sibelius Symphony #7

The best symphony ever written [stet].

[Note: after having written all this, I realize there are some good ones I’ve forgotten: Strauss’ Alpine Symphony, Vaughn Williams’ Sea Symphony, Rimsky Korsakov’s Scheherazade, Saint-Saëns’ Carnival of the Animals. I could probably justify not calling any of these symphonies per se (even the Sea Symphony sounds more like a cantata to me) but I’ll instead just call these honorable mentions. Having said that, they’re all very good, and if I wanted to spend another hour or so they’d bump Bruckner’s Symphony #1, Schumann’s Symphony #4, Beethoven’s Symphony #6, and Tchaikovsky’s Symphony #1 out of the top 100.]